# Cross Product

### a.k.a. the vector product

/ x1 / x2 / y1.z2 - y2.z1
u x v = u ^ v = | y1 x | y2 = | x2.z1 - x1.z2
\ z1 \ z2 \ x1.y2 - x2.y1

### u x v is a vector perpendicular to both u and v , which direction is given
by the usual right
handed rule, and the length, by :

|| u x v || = || u || . || v || . sin (uˆv)

### now we are able to get the angle ...

Before going further, let's check those properties (again
?)

#### u x v is normal to the plane defined by u and v (and a chosen point)

#### if ( i, j, k ) are the set of vectors that define your right handed three-dimensional
coordinate system, then k = i x j

/ 1 / 0 / 0.0 - 1.0 / 0
i x j = i ^ j = | 0 x | 1 = | 0.0 - 1.0 = | 0 = k
\ 0 \ 0 \ 1.1 - 0.0 \ 1

#### All the usual right handed rules could be applied, the
3 fingers, the thumb and the others, the screwdriver and the corkscrew for the
French ...

### Other simple problem : How to compute the normal to a plane ?